Question

Luisa began walking up a hill at a spot where the elevation is 0.9 km. After she walked

3 km, she saw a sign giving the elevation as 0.95 km. How far will she have walked when she
reaches and elevation of 1.1 km?

Answer 1

Luisa will have walked 9 km when she reaches an elevation of 1.1 km.

Step-by-step explanation:

To determine how far Luisa will have walked when she reaches an elevation of 1.1 km, we need to find the distance she has covered for each change in elevation. The elevation change between the starting point and the first sign is 0.95 km - 0.9 km = 0.05 km. The distance covered for this elevation change is 3 km. So, the distance covered per 0.05 km of elevation change is 3 km / 0.05 km = 60 km/km of elevation change.

Now, to find the distance covered for an elevation change of 0.15 km (1.1 km - 0.95 km), we can use the ratio we just found. The distance covered is (0.15 km) * (60 km/km of elevation change) = 9 km.

Therefore, Luisa will have walked 9 km when she reaches an elevation of 1.1 km.

Answer 2

3.82 km

Step-by-step explanation:

Assuming that the change in elevation is linear, we can calculate the elevation change per km traveled. The known values are the start (0km) and the sign (3km). The elevation gain over that interval is (0.95-9.0)km = 0.5km. That was for an distance interval of 3km, so we can write:

(0.5km elevation gain)/(3km distance)

We can use this as a rate change and and use it in a linear equation to predict the elevation as a function of distance.

Let y be the elevation and x the distance, both in km.

y = (0.183)(x)+b, where b is the elevation at the start of the trail. We can find b by using this equation and entering one of the two data points. Lets use the elevation of 0.95m at 3km distance:

y = (0.183)(x)+b

0.95 = (0.183)(3)+b

b = 0.4km

The full equation is :

y = (0.1833)X + 0.4

Enter 1.1 km for y and calculate x, the distance to reach 1.1 km altitude.

1.1 = (0.1833)X + 0.4

X = 3.82 km